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Simplifying x2 + -55x + 4 = 0 Reorder the terms: 4 + -55x + x2 = 0 Solving 4 + -55x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -55x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -55x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -55x + x2 = 0 + -4 -55x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -55x + x2 = -4 The x term is -55x. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55x + 756.25 + x2 = -4 + 756.25 Reorder the terms: 756.25 + -55x + x2 = -4 + 756.25 Combine like terms: -4 + 756.25 = 752.25 756.25 + -55x + x2 = 752.25 Factor a perfect square on the left side: (x + -27.5)(x + -27.5) = 752.25 Calculate the square root of the right side: 27.427176304 Break this problem into two subproblems by setting (x + -27.5) equal to 27.427176304 and -27.427176304.Subproblem 1
x + -27.5 = 27.427176304 Simplifying x + -27.5 = 27.427176304 Reorder the terms: -27.5 + x = 27.427176304 Solving -27.5 + x = 27.427176304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = 27.427176304 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = 27.427176304 + 27.5 x = 27.427176304 + 27.5 Combine like terms: 27.427176304 + 27.5 = 54.927176304 x = 54.927176304 Simplifying x = 54.927176304Subproblem 2
x + -27.5 = -27.427176304 Simplifying x + -27.5 = -27.427176304 Reorder the terms: -27.5 + x = -27.427176304 Solving -27.5 + x = -27.427176304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + x = -27.427176304 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + x = -27.427176304 + 27.5 x = -27.427176304 + 27.5 Combine like terms: -27.427176304 + 27.5 = 0.072823696 x = 0.072823696 Simplifying x = 0.072823696Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.927176304, 0.072823696}
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